Modern reasoning models depend on reasoning data, today sourced from human annotations or distilled from stronger LLMs. However, a rich and largely untapped source of supervision lies in expert systems (e.g., game engines, classical planners, theorem provers), which routinely produce near-optimal actions across diverse domains. But these experts are silent: they commit to an action without writing down the chain of thought (CoT) behind it. Recovering that CoT as natural-language reasoning would distill expert knowledge into a student that generalizes beyond the demonstrated actions. We treat it as a latent variable and study how to recover it from the action alone. Our approach, LeAct (Learning to reason from Actions), optimizes this latent variable: the student samples candidate CoTs for each expert action, and we retain those that measurably improve its own probability of recovering the action. Across imperfect-information games at multiple scales and a simulated robotics benchmark, LeAct reaches the solver's numerical floor on small enumerable games. At larger scale, it is 5× closer to the solver than the strongest expert-iteration baseline. At Flop Hold'em (∼109 infosets), LeAct wins head-to-head by +60 mbb/g, and on the robotics probe it is the only training recipe that improves on direct imitation. We present a principled framework and the result: expert systems become a categorically new source of reasoning teachers for foundation models.
A compact controller can coordinate stronger experts by selecting whom to consult, formulating requests, and integrating their responses. We study whether learning from both the controller's decisions and the experts' reasoning and code improves its generation after expert removal. We introduce \textsc{Rivet} for \emph{collaboration internalization}: expert-augmented reinforcement learning applies a shared outcome signal to controller decisions and returned expert spans, and verified trajectory internalization consolidates complete successful interactions through format-aware supervised training. The deployed controller generates reasoning, code, and interaction structure with local Python execution and no external LLM. Across seven competition-mathematics benchmarks, RIVET-1.7B and RIVET-4B achieve average accuracies of 28.25% and 44.16%; Stage~II improves RIVET-4B's accuracy after expert removal by 6.49 points, and GPQA-Diamond results provide evidence of generalization to scientific reasoning. Ablations show gains from ordinary trajectory supervision and additional format weighting, supporting the effectiveness of training on the content and structure of verified collaborations.
Language models can learn from experience, but raw solution trajectories are often too long and noisy to provide effective guidance. In this work, we propose Learning to Coach (L2C), a framework that trains a dedicated LLM-as-a-Coach to extract actionable experiential knowledge from an actor model's previous trajectory. The actor remains frozen, while the LLM-as-a-Coach is trained to maximize a reward given by the correctness of the actor's guided response. We study two such rewards: a same-instance reward, which improves subsequent responses on the original problem, and a cross-instance reward, which elicits knowledge that transfers to other instances. Across mathematical reasoning and interactive text-games, L2C consistently outperforms self-refinement and an untrained LLM-as-a-Coach. Running experiential learning for more iterations further improves accuracy and uses additional inference compute more effectively than enlarging the actor's decoding budget. The trained LLM-as-a-Coach also transfers to out-of-distribution tasks and adapts its guidance to the specific actor it coaches.
Training expert LLMs in domains with scarce data is difficult, often relying on multiple-choice questions (MCQs). However, standard outcome-based reinforcement learning (RL) on MCQs is risky. While it may improve accuracy, we observe it often degrades reasoning quality such as logical consistency. Existing solutions to supervise reasoning, such as large-scale Process Reward Models (PRMs), are prohibitively expensive. To address this, we propose CLARity, a cost-effective RL framework that enhances reasoning quality using only a small, general-purpose LLM. CLARity integrates a consistency-aware reward mechanism with a 2-stage refine-then-monitor training pipeline to enhance reasoning consistency, and a dynamic data reformulation strategy to to better exploit limited data. Experiments demonstrate that CLARity improves response consistency by 16.5% and accuracy by 7.5% over baselines. Human evaluations further confirm holistic improvements in coherence and professionalism. Thus, CLARity offers a generalizable solution that enables smaller models to effectively guide expert models by reasoning consistency. Our code is open sourced at: https://github.com/Infinite-set/CLARity